Generic Expression Hardness Results for Primitive Positive Formula Comparison
Simone Bova, Hubie Chen, Matthew Valeriote
TL;DR
This paper investigates the computational complexity of equivalence and containment problems for primitive positive formulas over finite structures, establishing generic hardness results and suggesting a comprehensive complexity classification.
Contribution
It introduces two generic hardness results for formula comparison problems and provides evidence for their optimality and a potential complexity trichotomy.
Findings
Established generic hardness results for equivalence and containment
Provided evidence supporting the optimality of these results
Suggested a possible complexity trichotomy for the problems
Abstract
We study the expression complexity of two basic problems involving the comparison of primitive positive formulas: equivalence and containment. In particular, we study the complexity of these problems relative to finite relational structures. We present two generic hardness results for the studied problems, and discuss evidence that they are optimal and yield, for each of the problems, a complexity trichotomy.
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Taxonomy
Topicssemigroups and automata theory · Logic, programming, and type systems · Complexity and Algorithms in Graphs